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You could also go into the Statistics tab within the game and look at the range and effectivness of your units from there. It is pretty useful in explaining some things that might not be apparent right away when just looking at individual units.
Statistics tab is the easiest to use. You can click on the columns there to sort the tables.
As to knowing distances between provinces: no way except using airplanes based at starting point. So if you want to see whether an air transport is within range, either rebase the air transport to what seems to be the closest base, or rebase any other air wing to that airbase. Then click on any air mission and the range will be revealed.